In recent years, deep learning-based quantum state estimation (QSE) has attracted extensive attention, and the generative adversarial network (GAN) is a popular model in the field of deep learning. In this paper, we apply GANs into the field of QSE and design a custom neural network layer which makes the original network outputs satisfy quantum state constraints. It is worth noting that our designed custom neural-network layers are applicable to arbitrary feed-forward neural networks used for QSE. GANs are trained and tested by randomly generated pure state density matrices. Simulation results show that the designed neural network estimator is capable of achieving a fidelity higher than 99% for both eigenstates and superposition states.
In recent years, deep learning-based quantum state estimation (QSE) has attracted extensive attention, and the generative adversarial network (GAN) is a popular model in the field of deep learning. In this paper, we apply GANs into the field of QSE and design a custom neural network layer which makes the original network outputs satisfy quantum state constraints. It is worth noting that our designed custom neural-network layers are applicable to arbitrary feed-forward neural networks used for QSE. GANs are trained and tested by randomly generated pure state density matrices. Simulation results show that the designed neural network estimator is capable of achieving a fidelity higher than 99% for both eigenstates and superposition states.
Tremendous progress has been witnessed in artificial intelligence where neural network backed deep learning systems have been used, with applications in almost every domain. As a representative deep learning framework, Generative Adversarial Network (GAN) has been widely used for generating artificial images, text-to-image or image augmentation across areas of science, arts and video games. However, GANs are computationally expensive, sometimes computationally prohibitive. Furthermore, training GANs may suffer from convergence failure and modal collapse. Aiming at the acceleration of use cases for practical quantum computers, we propose QuGAN, a quantum GAN architecture that provides stable convergence, quantum-states based gradients and significantly reduced parameter sets. The QuGAN architecture runs both the discriminator and the generator purely on quantum state fidelity and utilizes the swap test on qubits to calculate the values of quantum-based loss functions. Built on quantum layers, QuGAN achieves similar performance with a 94.98% reduction on the parameter set when compared to classical GANs. With the same number of parameters, additionally, QuGAN outperforms state-of-the-art quantum based GANs in the literature providing a 48.33% improvement in system performance compared to others attaining less than 0.5% in terms of similarity between generated distributions and original data sets. QuGAN code is released at https://github.com/yingmao/Quantum-Generative-Adversarial-Network
Tremendous progress has been witnessed in artificial intelligence, where neural network backed deep learning systems have been used, with applications in almost every domain. As a representative deep learning framework, Generative Adversarial Network (GAN) has been widely used for generating artificial images, text-to-image or image augmentation across areas of science, arts and video games. However, GANs are computationally expensive, sometimes computationally prohibitive. Furthermore, training GANs may suffer from convergence failure and modal collapse. Aiming at the acceleration of use cases for practical quantum computers, we propose QuGAN, a quantum GAN architecture that provides stable convergence, quantum-states based gradients and significantly reduced parameter sets. The QuGANarchitecture runs both the discriminator and the generator purely on quantum state fidelity and utilizes the swap test on qubits to calculate the values of quantum-based loss functions. Built on quantum layers, QuGAN achieves similar performance with a 94.98% reduction on the parameter set when compared to classical GANs. With the same number of parameters, addition-ally, QuGAN outperforms state-of-the-art quantum based GANsin the literature providing a 48.33% improvement in system performance compared to others attaining less than 0.5% in terms of similarity between generated distributions and original data sets.
Quantum state tomography (QST) is a challenging task in intermediate-scale quantum devices. Here, we apply conditional generative adversarial networks (CGANs) to QST. In the CGAN framework, two dueling neural networks, a generator and a discriminator, learn multimodal models from data. We augment a CGAN with custom neural-network layers that enable conversion of output from any standard neural network into a physical density matrix. To reconstruct the density matrix, the generator and discriminator networks train each other on data using standard gradient-based methods. We demonstrate that our QST-CGAN reconstructs optical quantum states with high fidelity, using orders of magnitude fewer iterative steps, and less data, than both accelerated projected-gradient-based and iterative maximum-likelihood estimation. We also show that the QST-CGAN can reconstruct a quantum state in a single evaluation of the generator network if it has been pretrained on similar quantum states.
We apply deep-neural-network-based techniques to quantum state classification and reconstruction. Our methods demonstrate high classification accuracies and reconstruction fidelities, even in the presence of noise and with little data. Using optical quantum states as examples, we first demonstrate how convolutional neural networks (CNNs) can successfully classify several types of states distorted by, e.g., additive Gaussian noise or photon loss. We further show that a CNN trained on noisy inputs can learn to identify the most important regions in the data, which potentially can reduce the cost of tomography by guiding adaptive data collection. Secondly, we demonstrate reconstruction of quantum-state density matrices using neural networks that incorporate quantum-physics knowledge. The knowledge is implemented as custom neural-network layers that convert outputs from standard feed-forward neural networks to valid descriptions of quantum states. Any standard feed-forward neural-network architecture can be adapted for quantum state tomography (QST) with our method. We present further demonstrations of our proposed QST technique with conditional generative adversarial networks (QST-CGAN) [Ahmed et al., Phys. Rev. Lett. 127, 140502 (2021)]. We motivate our choice of a learnable loss function within an adversarial framework by demonstrating that the QST-CGAN outperforms, across a range of scenarios, generative networks trained with standard loss functions. For pure states with additive or convolutional Gaussian noise, the QST-CGAN is able to adapt to the noise and reconstruct the underlying state. The QST-CGAN reconstructs states using up to two orders of magnitude fewer iterative steps than iterative and accelerated projected-gradient-based maximum-likelihood estimation (MLE) methods. We also demonstrate that the QST-CGAN can reconstruct both pure and mixed states from two orders of magnitude fewer randomly chosen data points than these MLE methods. Our paper opens possibilities to use state-of-the-art deep-learning methods for quantum state classification and reconstruction under various types of noise.
Tremendous progress has been witnessed in artificial intelligence within the domain of neural network backed deep learning systems and its applications. As we approach the post Moore’s Law era, the limit of semiconductor fabrication technology along with a rapid increase in data generation rates have lead to an impending growing challenge of tackling newer and more modern machine learning problems. In parallel, quantum computing has exhibited rapid development in recent years. Due to the potential of a quantum speedup, quantum based learning applications have become an area of significant interest, in hopes that we can leverage quantum systems to solve classical problems. In this work, we propose a quantum deep learning architecture; we demonstrate our quantum neural network architecture on tasks ranging from binary and multi-class classification to generative modelling. Powered by a modified quantum differentiation function along with a hybrid quantum-classic design, our architecture encodes the data with a reduced number of qubits and generates a quantum circuit, loading it onto a quantum platform where the model learns the optimal states iteratively. We conduct intensive experiments on both the local computing environment and IBM-Q quantum platform. The evaluation results demonstrate that our architecture is able to outperform Tensorflow-Quantum by up to 12.51% and 11.71% for a comparable classic deep neural network on the task of classification trained with the same network settings. Furthermore, our GAN architecture runs the discriminator and the generator purely on quantum hardware and utilizes the swap test on qubits to calculate the values of loss functions. In comparing our quantum GAN, we note our architecture is able to achieve similar performance with 98.5% reduction on the parameter set when compared to classical GANs. With the same number of parameters, additionally, QuGAN outperforms other quantum based GANs in the literature for up to 125.0% in terms of similarity between generated distributions and original data sets.
The increasing success of classical generative adversarial networks (GANs) has inspired several quantum versions of GANs. Fully quantum mechanical applications of such quantum GANs have been limited to one- and two-qubit systems. In this paper, we investigate the entangling quantum GAN (EQ-GAN) for multiqubit learning. We show that the EQ-GAN can learn a circuit more efficiently compared with a swap test. We also consider the EQ-GAN for learning eigenstates that are variational quantum eigensolver (VQE) approximated and find that it generates excellent overlap matrix elements when learning VQE states of small molecules. However, this does not directly translate into a good estimate of the energy due to a lack of phase estimation. Finally, we consider random state learning with the EQ-GAN for up to six qubits, using different two-qubit gates, and show that it is capable of learning completely random quantum states, something which could be useful in quantum state loading.